Amazon typically plays its customer data close to the chest, but on Monday, the e-commerce giant let a few figures about its Prime service trickle out.

The Prime service, an offering combining free two-day shipping on many items with access to video streaming, had a "record-setting" holiday, an Amazon press release said. More than 3 million members joined the service in the third week of December, bringing its total membership to "tens of millions," it said.

Amazon also said it sold "millions" of its devices, doubling last year's device sales, although it didn't provide a more exact figure. Among the company's devices, its Fire tablet computer was the best-selling and was also the "most gifted and most wished-for" since its introduction 15 weeks ago, it said.

Amazon also said its Fire tablet, Amazon Echo and Fire TV Stick were three of the top five items ordered on Christmas Eve through the Prime Now service — its one-hour delivery service available to in certain U.S. regions. The online retailer also said that Christmas Eve was its biggest day ever for Prime Now.

When the Fire tablet was launched in September with a $49.99 price tag, analysts noted that there were few comparable offerings at that price point, Reuters reported. Indeed, at the time, one analyst called the tablet "a gateway drug" for the Prime service, Reuters reported.

The company has had mixed success with creating devices. Last year, Amazon had to take a $170 million write-down on its slow-moving inventory of $200 Fire smartphones, Reuters reported. Amazon discontinued the Fire smartphone in September.

Amazon also highlighted Monday that 200 million more items received free shipping this year, reaching a record. It added that holiday viewing hours of its Prime service's video-streaming doubled from a year earlier and music streaming globally rose 350 percent on the year.

The company has been aiming to boost viewership on its streaming service, with media reports saying it plans to produce 16 feature films a year. Amazon founder Jeff Bezos told Die Welt recently, "we want to win an Oscar." Its original offerings have already been nominated for 40 awards this year, including five Golden Globe nominations, Amazon said Monday.

It released its first original movie, "Chi-Raq" from director Spike Lee, earlier this month.

Amazon doesn't generally reveal much about its customer data. Earlier this month, Macquarie Capital analyst Ben Schachter told CNBC that his company estimated that around 25 percent of U.S. homes had already signed up for the Prime service. Macquarie estimates that by year-end, Amazon will capture 51 percent of U.S. e-commerce growth and 24 percent of retail growth.

The company can have a huge influence over online shopping in general. Earlier this month, the latest CNBC All-America Economic Survey found that 40 percent of all adults search Amazon "always" or "most of the time" when shopping online, compared to just 10 percent who say they never include Amazon in an online search.

Other figures from the survey were more striking: The conversion rate, or the number of visits to the website that result in a purchase, is massive. Some 50 percent of those Americans searching Amazon most frequently are actually making a purchase. That compares with the widely cited retail industry average for turning online searches into purchases at a mere 3 percent.